How to create/animate a Theraband?
Use a hooked cloth


Create a base mesh approximately the shape of a relaxed band with some subdivision (at least 4/5 vertices along its width, and around a hundred across):



... a couple subdivisions and a mirror later:



(hint: maybe I made it too relaxed. Make it tighter or it'll be very floppy during the simulation)
Select a bunch of vertices in the "hand" region, CtrlH > "Hook to New Object". This will create an Empty.



Repeat for the other hand
Select both the hooked regions, create a new Vertex Group and "Assign" these vertices to it


Create the other objects that will interact with your band (like: a foot, a floor) and select "Collision" from the Physics tab for each of them.

 
Animate the Empties (from step 2) according to the hand's motion
Select the rubber band, apply "Cloth" from the Physics menu. Use the Rubber preset but increase both the Structural and the Steps values. Enable "Pinning" and select the Vertex Group created at step 3. Increase also the Collision Quality. You can increase the Structural (how "hard" the band is) further, but every time you do so you should also increase Steps and Collision Quality.


Bake the Cloth Cache or just play the animation (AltA)